Divergence Properties of the Brown-Thompson's groups and the braided Thompson's groups

Abstract: Golan and Sapir proved that the Thompson's groups $F$, $T$ and $V$ have linear divergence. In this talk, we focus on the divergence properties of several generalisation of the Thompson's groups, we first consider the Brown-Thompson's groups $F_n$, $T_n$ and $V_n$ and found out that these groups also have linear divergence function. We then consider the braided Thompson's groups $BF$ and $\widehat{BF}$ and $\widehat{BV}$ together with Kodama's result on the linear divergence of $BV$, we conclude that the braided Thompson's groups have linear divergence.

group theory

Audience: researchers in the topic

World of GroupCraft